Theorem wunot

Description: A weak universe is closed under ordered triples. (Contributed by Mario Carneiro, 2-Jan-2017)

	Ref	Expression
Hypotheses	wun0.1	|- ( ph -> U e. WUni )
	wunop.2	|- ( ph -> A e. U )
	wunop.3	|- ( ph -> B e. U )
	wunot.3	|- ( ph -> C e. U )
Assertion	wunot	|- ( ph -> <. A , B , C >. e. U )

Proof

Step	Hyp	Ref	Expression
1		wun0.1	|- ( ph -> U e. WUni )
2		wunop.2	|- ( ph -> A e. U )
3		wunop.3	|- ( ph -> B e. U )
4		wunot.3	|- ( ph -> C e. U )
5		df-ot	|- <. A , B , C >. = <. <. A , B >. , C >.
6	1 2 3	wunop	|- ( ph -> <. A , B >. e. U )
7	1 6 4	wunop	|- ( ph -> <. <. A , B >. , C >. e. U )
8	5 7	eqeltrid	|- ( ph -> <. A , B , C >. e. U )